Study of impulsive problems under Mittag-Leffler power law

Authors :: Thabet Abdeljawad
Kamal Shah
Fahd Jarad
Mohammed S. Abdo
Source :: Heliyon, Vol 6, Iss 10, Pp e05109-(2020), Heliyon
Publication Year :: 2020
Publisher :: Elsevier BV, 2020.
Abstract: This article is fundamentally concerned with deriving the solution formula, existence, and uniqueness of solutions of two types of Cauchy problems for impulsive fractional differential equations involving Atangana-Baleanu-Caputo (ABC) fractional derivative which possesses nonsingular Mittag-Leffler kernel. Our investigation is based on nonlinear functional analysis and some fixed point techniques. Besides, some examples are given delineated to illustrate the effectiveness of our outcome.<br />Mathematics; Fractional impulsive problems; Atangana-Baleanu-Caputo operator; Existence theory; Fixed point theorem